Dynamics of a higher dimensional analog of the trigonometric functions

Abstract

We introduce a higher dimensional quasiregular map analogous to the trigonometric functions and we use the dynamics of this map to define, for d>1, a partition of d-dimensional Euclidean space into curves tending to infinity such that two curves may intersect only in their endpoints and such that the union of the curves without their endpoints has Hausdorff dimension one.

12 pages

References in corpus (1)

• Quasiregular dynamics on the n-sphere

Cited by in corpus (8)

• Fatou-Julia theory for non-uniformly quasiregular maps
• Foundations for an iteration theory of entire quasiregular maps
• The Julia set and the fast escaping set of a quasiregular mapping
• The escaping set in transcendental dynamics
• Quasiregular mappings of polynomial type in R^2
• Dynamics of mappings with constant dilatation
• Iteration of quasiregular tangent functions in three dimensions
• Chaotic dynamics of a quasiregular sine mapping